Primality proof for n = 599219167:

Take b = 2.

b^(n-1) mod n = 1.

20707 is prime.
b^((n-1)/20707)-1 mod n = 5330079, which is a unit, inverse 512598205.

53 is prime.
b^((n-1)/53)-1 mod n = 147598986, which is a unit, inverse 123777092.

(53 * 20707) divides n-1.

(53 * 20707)^2 > n.

n is prime by Pocklington's theorem.